Well, just like the ulterior motives ascribed to Baron Haussmann's renovation of Paris, a new capital that is more spread out and auto-oriented is also harder to protest and riot in. That's not to say it doesn't happen - lots of protesting in Rio and Sao Paulo recently despite the capital being moved to the auto-oriented Brasilia decades ago. But it doesn't shut down the government when that happens.
Political motivations aside, this fits into a much larger and longer-term movement to decentralize Cairo. The city as a whole is
denser than Manhattan at 40000 p/km^2, with older neighborhoods in the 60000-100000 p/km^2 range. However, it has none of the infrastructure of Manhattan - just three overtaxed subway lines providing poor coverage to the city as a whole, and a confusing network of buses on massively congested roads.
It doesn't surprise me that they feel the need to decentralize into the desert. It should be done at responsible density levels with appropriate transit infrastructure and measures to conserve energy, however, and the plans I've seen have been more reminiscent of Dubai or China-style planning than French or Canadian.